Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE LIMITING DIFFUSION OF SPECIAL DIPLOID MODEL IN POPULATION GENETICS

  • CHOI, WON (DEPARTMENT OF MATHEMATICS, UNIVERSITY OF INCHEON)
  • Published : 2005.05.01
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Abstract

In this note, we characterize the limiting diffusion of a diploid model by defining the discrete generator for the resealed Markov chain. We conclude that this limiting diffusion model is with uncountable state space and mutation selection and special 'mutation or gene conversion rate'.

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References

  1. W. Choi and B. K. Lee, On the diffusion processes and their applications in population genetics, J. Appl. Math. Comput. 15 (2004), no. 1-2 https://doi.org/10.1007/BF02935744
  2. W. Choi, The application of stochastic analysis to countable allelic diffusion model, Bull. Korean Math. Soc. 41 (2004), no. 2, 337-345 https://doi.org/10.4134/BKMS.2004.41.2.337
  3. D. A. Dawson, Geostochastic calculus, Canad. J. Statist. 6 (1978), 143-168 https://doi.org/10.2307/3315044
  4. S. N. Ethier and T. G. Kurtz, The infinitely-many-alleles model with selection as a measure-valued diffusion, in stochastic methods in biology, proceedings, Nagoya, Japan, 1985
  5. J. H. Gillespie, Natural selection for within-generation variance in offspring num- ber, Genetics, 76 (1974), 601-606
  6. J. Roughgarden, Theory of population genetics and evolutionary ecology : An Introduction, Macmillan Publishing Co., 1979

Cited by

  1. ON THE MARTINGALE PROPERTY OF LIMITING DIFFUSION IN SPECIAL DIPLOID MODEL vol.31, pp.1_2, 2013, https://doi.org/10.14317/jami.2013.241
  2. ON THE MARTINGALE EXTENSION OF LIMITING DIFFUSION IN POPULATION GENETICS vol.22, pp.1, 2014, https://doi.org/10.11568/kjm.2014.22.1.29